Crippling Chill can target a creature that's already tapped. It still won't untap during its controller's next untap step.

5/1/2012

Crippling Chill tracks the creature, but not its controller. If the creature changes controllers before its first controller's next untap step has come around, then it won't untap during its new controller's next untap step.

9/20/2014

Crippling Chill can target a creature that’s already tapped. It still won’t untap during its controller’s next untap step.

9/20/2014

Crippling Chill tracks the creature, but not its controller. If the creature changes controllers before its first controller’s next untap step has come around, then it won’t untap during its new controller’s next untap step.